Scenario's berekend
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@ -391,4 +391,7 @@ TSWLatexianTemp*
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#*Notes.bib
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# Ignore KiCad backups
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*-backups/
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*-backups/
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# Ignore draw.io backups
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*.drawio.bkp
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@ -0,0 +1,540 @@
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|
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257
doc/main.tex
257
doc/main.tex
|
|
@ -1,46 +1,17 @@
|
|||
\documentclass[10pt]{article}
|
||||
\documentclass{article}
|
||||
|
||||
\usepackage[english]{babel}
|
||||
% \usepackage[a4paper,top=2cm,bottom=2cm,left=2cm,right=2cm,marginparwidth=1.75cm]{geometry}
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\usepackage[a4paper, total={7in, 10in}]{geometry}
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\usepackage[a4paper,top=2cm,bottom=2cm,left=2cm,right=2cm,marginparwidth=1.75cm]{geometry}
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\usepackage[inline]{enumitem}
|
||||
\usepackage{amsmath}
|
||||
\usepackage{multicol}
|
||||
\usepackage{lipsum}
|
||||
\usepackage{caption}
|
||||
\usepackage{textcomp}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{enumitem}
|
||||
\usepackage{listings}
|
||||
\usepackage{xcolor}
|
||||
|
||||
\newenvironment{Figure}
|
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{\par\medskip\noindent\minipage{\linewidth}}
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{\endminipage\par\medskip}
|
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|
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\definecolor{codegreen}{rgb}{0,0.6,0}
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\definecolor{codegray}{rgb}{0.5,0.5,0.5}
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\definecolor{codepurple}{rgb}{0.58,0,0.82}
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\definecolor{backcolour}{rgb}{0.97,0.97,0.95}
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\lstdefinestyle{mystyle}{
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backgroundcolor=\color{backcolour},
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commentstyle=\color{codegreen},
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keywordstyle=\color{magenta},
|
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numberstyle=\tiny\color{codegray},
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stringstyle=\color{codepurple},
|
||||
basicstyle=\ttfamily\footnotesize,
|
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breakatwhitespace=false,
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breaklines=true,
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captionpos=b,
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keepspaces=true,
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||||
numbers=left,
|
||||
numbersep=5pt,
|
||||
showspaces=false,
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showstringspaces=false,
|
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showtabs=false,
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tabsize=2
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||||
}
|
||||
|
||||
\lstset{style=mystyle}
|
||||
|
||||
\graphicspath{{images/}}
|
||||
\usepackage{float}
|
||||
\usepackage{lipsum}
|
||||
\usepackage{hyperref}
|
||||
\usepackage{listings}
|
||||
|
||||
\title{Euro Rover}
|
||||
|
||||
|
|
@ -50,33 +21,205 @@
|
|||
\and
|
||||
van Vliet, Stein\\
|
||||
Student Nr: 1811402
|
||||
}
|
||||
}
|
||||
|
||||
\makeindex
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
\section{Inleiding}
|
||||
De Hogeschool Utrecht werkt samen met andere hogescholen voor het ontwikkelen van een Euro Moon Rover. Hiervoor is ee Aan deze rover zijn een aantal eisen verbonden
|
||||
\begin{abstract}
|
||||
Onderzoeksverlag naar een passende motor en tandwieloverbrenging voor de Euro Rover. In dit document wordt onderzocht of de voorgestelde motor en tandwieloverbrenging voldoet aan de eisen van de rover.
|
||||
\end{abstract}
|
||||
|
||||
\section{Onderzoeks}
|
||||
Voor de Eurorover is een set van motor en tandwieloverbrenging voorgesteld, het gaat om de RE25 1187xx motor en de Planetary Gearhead GP xx xx van de firma Maxon.
|
||||
In dit document wordt onderzocht of dat de voorgestelde motor en tandwieloverbrenging voldoet aan de eisen van de rover. Hiervoor zullen de volgende eigenschappen worden onderzocht:
|
||||
\begin{itemize}
|
||||
\item De lasteisen/-wensen
|
||||
\item De mechanische transmissie
|
||||
\item De motor
|
||||
\item De efficiëntie
|
||||
\noindent\makebox[\linewidth]{\rule{\linewidth}{0.4pt}}
|
||||
\setlist[itemize]{itemjoin=\hspace*{\fill},itemjoin*=\hspace*{\fill}}
|
||||
|
||||
\begin{multicols}{2}
|
||||
|
||||
\section{Inleiding}
|
||||
\colorbox{red}{TODO}
|
||||
De Hogeschool Utrecht werkt samen met andere hogescholen voor het ontwikkelen van een Euro Moon Rover.
|
||||
|
||||
\section{Onderzoek}
|
||||
\colorbox{red}{TODO}
|
||||
Voor de Eurorover is een set van motor en tandwieloverbrenging voorgesteld, het gaat om de RE25 1187xx motor en de Planetary Gearhead GP xx xx van de firma Maxon.
|
||||
In dit document wordt onderzocht of dat de voorgestelde motor en tandwieloverbrenging voldoet aan de eisen van de rover.
|
||||
|
||||
\subsection{Eigenschappen}
|
||||
De kar heeft de volgende eigenschappen:
|
||||
\begin{align*}
|
||||
m_{rover} &= 6 & [kg] \\
|
||||
w &= 400 & [mm] \\
|
||||
l &= 250 & [mm] \\
|
||||
\alpha_{typ} &= 20 & [deg] \\
|
||||
\alpha_{max} &= 30 & [deg]
|
||||
\end{align*}
|
||||
|
||||
De wielen hebben de volgende eigenschappen:
|
||||
\begin{align*}
|
||||
r &= 0.15 & [m] \\
|
||||
\mu_s &= 0,9 & [-] \\
|
||||
C_r &= 0,1 & [-]
|
||||
\end{align*}
|
||||
|
||||
Met de aandrijving moeten de volgende eisen worden voldaan:
|
||||
\begin{align*}
|
||||
v_{max} &= 2.1 & [m/s] \\
|
||||
a_{acc} &= 0.7 & [m/s^2] \\
|
||||
a_{dec} &= 0.5 & [m/s^2]
|
||||
\end{align*}
|
||||
|
||||
|
||||
\section{Lasteisen/-wensen}
|
||||
Om te bepalen wat de maximale lasteisen/-wensen van de motor zijn, worden de eisen van de rover onder verschillende scenario's verdeeld. De rover moet in staat zijn om te accelereren, constant te rijden en te deaccelereren op;
|
||||
\begin{itemize}
|
||||
\item een vlakke ondergrond
|
||||
\item een opgaande helling van 20 graden
|
||||
\item een neergaande helling van 20 graden
|
||||
\end{itemize}
|
||||
\section{Lasteisen/-wensen}
|
||||
Om te bepalen wat de maximale lasteisen/-wensen van de motor zijn, worden de eisen van de rover onder verschillende scenario's verdeeld. De rover moet in staat zijn om te versnellen, constant te rijden en te vertragen op:
|
||||
\begin{itemize}
|
||||
\item een vlakke ondergrond
|
||||
\end{itemize}
|
||||
|
||||
De rover moet constant de maximum snelheid kunnen rijden op:
|
||||
\begin{itemize}
|
||||
\item een opgaande helling van 20 graden
|
||||
\item een neergaande helling van 20 graden
|
||||
\end{itemize}
|
||||
|
||||
De rover is in staat om, op elk gegeven oppervlak, het gewicht eerlijk over de wielen te verdelen; Dit maakt het mogelijk om de lasten voor slechts één wiel te berekenen. In het volgende hoofdstuk worden deze scenario's verder uitgewerkt. Het zwaarste resultaat bepaalt het type motor dat gebruikt zal worden. Omdat het gewicht van de rover wordt verdeeld over de wielen, zal het volgende gewicht worden gebruikt in de berekeningen
|
||||
\begin{align*}
|
||||
m &= \frac{m_{rover}}{4}\\
|
||||
&= \frac{6}{4}\\
|
||||
&= 1.5 & [kg]
|
||||
\end{align*}
|
||||
|
||||
\section{Scenario's}
|
||||
In dit hoofdstuk worden afbeeldingen gebruikt om de verschillende scenario's te visualiseren. Deze afbeeldingen zijn niet op schaal.
|
||||
|
||||
$F_{eff}$ is het resultaat van de aandrijving ($F_{aand}$) min de rolweerstand ($F_{rol}$) en eventueel een component van de zwaartekracht ($F_{z}$). De gewenste versnelling bepaalt de nodige resulterende kracht met de volgende formule:
|
||||
\begin{equation}
|
||||
F_{eff} = m \cdot a
|
||||
\end{equation}
|
||||
|
||||
\subsection{Vlakke ondergrond}
|
||||
\begin{figure}[H]
|
||||
\includegraphics[width=\linewidth]{./res/s1.png}
|
||||
\caption{Vlakke ondergrond, bewegingsrichting rechts}
|
||||
\label{fig:s_flat}
|
||||
\end{figure}
|
||||
|
||||
\subsubsection{Constante snelheid}
|
||||
Voor de constante snelheid geldt dat $a = 0\ [ms^{-2}]$ dus $F_{eff} = 0\ [N]$. De enige kracht die overblijft is de rolweerstand. De aandrijvingskracht $F_{aand}$ moet gelijk zijn aan de rolweerstand $F_{rol}$.
|
||||
|
||||
De rolweerstand is afhankelijk van de normaalkracht $F_N$, $F_N$ is in dit geval gelijk aan de zwaartekracht $F_z$ dus:
|
||||
\begin{align*}
|
||||
F_N &= F_z \\
|
||||
F_z &= m \cdot g \\
|
||||
&= 1.5 \cdot 9.81 \\
|
||||
&= 14.715 & [N]\\
|
||||
\\
|
||||
F_{rol} &= C_r \cdot F_N\\
|
||||
&= 0.1 \cdot 14.715 \\
|
||||
&= 1.4715 & [N]\\
|
||||
\\
|
||||
F_{aand} &= F_{rol}
|
||||
\end{align*}
|
||||
|
||||
\subsubsection{Versnellen}
|
||||
\begin{align*}
|
||||
F_{eff} &= m \cdot a \\
|
||||
&= 1.5 \cdot 0.7 \\
|
||||
&= 1.05 & [N] \\
|
||||
\\
|
||||
F_{aand} &= F_{eff} + F_{rol} \\
|
||||
&= 1.05 + 1.4715 \\
|
||||
&= 2.5215 & [N]
|
||||
\end{align*}
|
||||
|
||||
\subsubsection{Vertragen}
|
||||
\begin{align*}
|
||||
F_{eff} &= m \cdot a \\
|
||||
&= 1.5 \cdot 0.5 \\
|
||||
&= 0.75 & [N] \\
|
||||
\\
|
||||
F_{aand} &= F_{rol} - F_{eff} \\
|
||||
&= 1.4715 - 0.75 \\
|
||||
&= 0.7215 & [N]
|
||||
\end{align*}
|
||||
|
||||
\subsection{Dalende ondergrond}
|
||||
\begin{figure}[H]
|
||||
\includegraphics[width=\linewidth]{./res/s2.png}
|
||||
\caption{Dalende ondergrond, bewegingsrichting rechts}
|
||||
\label{fig:s_fall}
|
||||
\end{figure}
|
||||
|
||||
In dit geval is de zwaartekracht niet haaks aan de ondergrond, de zwaartekracht verdeelt zich in een component loodrecht op de ondergrond een een component parallel aan de ondergrond. De component loodrecht op de ondergrond is gelijk aan de normaalkracht $F_N$.
|
||||
|
||||
\begin{align*}
|
||||
F_{z} &= m \cdot g \\
|
||||
&= 1.5 \cdot 9.81 \\
|
||||
&= 14.715 & [N] \\
|
||||
\\
|
||||
\alpha &= 20 & [deg] \\
|
||||
\\
|
||||
F_N &= F_{z1} \\
|
||||
F_{z1} &= \cos{\alpha}\cdot F_{z}\\
|
||||
&= \cos{20}\cdot 14.715 \\
|
||||
&= 13.743 & [N] \\
|
||||
F_{z2} &= \sin{\alpha}\cdot F_{z}\\
|
||||
&= \sin{20}\cdot 14.715 \\
|
||||
&= 5.03 & [N] \\
|
||||
\end{align*}
|
||||
|
||||
De rolweerstand in dit geval is:
|
||||
\begin{align*}
|
||||
F_{rol} &= C_r \cdot F_N\\
|
||||
&= 0.1 \cdot 13.743 \\
|
||||
&= 1.3743 & [N]
|
||||
\end{align*}
|
||||
|
||||
Voor een constante snelheid dient $F_{eff}$ nul te zijn dus:
|
||||
\begin{align*}
|
||||
F_{eff} &= F_{aand} + F_{z2} - F_{rol} = 0\\
|
||||
&= F_{aand} + 5.03 - 1.3743 = 0\\
|
||||
F_{aand} &= 1.3743 - 5.03\\
|
||||
&= -3.6557 & [N]
|
||||
\end{align*}
|
||||
|
||||
De motor moet in dit geval dus tegenkracht leveren om de kar op en constante snelheid te houden.
|
||||
|
||||
\subsection{Stijgende ondergrond}
|
||||
\begin{figure}[H]
|
||||
\includegraphics[width=\linewidth]{./res/s3.png}
|
||||
\caption{Stijgende ondergrond, bewegingsrichting rechts}
|
||||
\label{fig:s_rise}
|
||||
\end{figure}
|
||||
In dit scenario werkt de zwaartekracht tegen de aandrijving, de rest blijft hetzelfde als bij de dalende ondergrond. Voor $F_{aand}$ geldt:
|
||||
|
||||
\begin{align*}
|
||||
F_{eff} &= F_{aand} - F_{z2} - F_{rol} = 0\\
|
||||
F_{aand} &= F_{z2} + F_{rol}\\
|
||||
&= 5.03 + 1.3743\\
|
||||
&= 6.4043 & [N]
|
||||
\end{align*}
|
||||
|
||||
\subsection{Slip}
|
||||
In de eigenschappen van de wielen is de statische wrijvingscoëfficiënt $\mu_s$ gegeven. $F_{eff}$ mag niet groter zijn dan de maximale statische wrijvingskracht $F_{s,max}$. De maximale statische wrijvingskracht in dit geval is:
|
||||
\begin{align*}
|
||||
F_{s,max} &= \mu_s \cdot F_N \\
|
||||
&= 0.9 \cdot 14.715 \\
|
||||
&= 13.2435 & [N]
|
||||
\end{align*}
|
||||
|
||||
Als $F_{eff}$ groter is dan $F_{s,max}$ zal er slip optreden. In dit geval moet de aandrijvingskracht $F_{eff}$ gelijk zijn aan $F_{s,max}$.
|
||||
|
||||
Er is geen van de scenario's sprake van slip.
|
||||
|
||||
\section{Selectie}
|
||||
Uit de besproken scenario's is gebleken dat de maximale aandrijvingskracht benodigd om aan de eisen te voldoen gelijk is aan $6.4043\ [N]$.
|
||||
|
||||
\section{Conclusie}
|
||||
\colorbox{red}{TODO}
|
||||
|
||||
|
||||
|
||||
\end{multicols}
|
||||
\end{document}
|
||||
|
|
|
|||
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Reference in New Issue